Chemistry - A Molecular Science

Chapter 2 Quantum Theory

36

information, each of which must be anal

yzed to get the best picture possible.

The ‘picture’ that scientists obtain is called the

spectrum

of the atom or molecule: a

plot of how much light is absorbed or emitted

versus

the wavelength or frequency of the

light. Scientists analyze the spectrum of a s

ubstance to determine its composition or to

better understand its properties. For example, scientists have long used atomic spectra to determine the composition of a mixture and to identify the presence of elements in distant stars. The study of atomic and molecular spectra is called

spectroscopy

.

Let us begin our discussion of atomic spectra with the observation that high-energy

electrons in a gas discharge tube can cause certa

in gases contained in the tube to glow with

characteristic colors. For example, neon, a co

lorless gas in the absen

ce of the high-energy

electrons, glows bright red when a voltage is

applied across a discharge tube containing

neon (

i.e

., a neon light). Recall that white light consists of all colors, so it produces a

continuous spectrum

, similar to the one shown at the top of Figure 2.4, as the colors merge

continuously into one another. However, the light observed from the gas in a discharge tube consists of only a

few colors

, which

are separated from one another, to produce a

line

spectrum

. Each

line

of a line spectrum represents one of the component

colors

of the

observed glow.

400

700

600

500

Prism

nm

= 410.3 nml

= 432.4 nml

= 486.3 nml

= 656.4 nml

HydrogenDischargeTube

Continuous

Line

Figure 2.4 A continuous and a line spectrum The spectrum at the top is a c

ontinuous spectrum that would be

obtained with white light, while the line spectrum below it would be obtained from a hydrogen discharge tube.

Figure 2.4 represents the experiment in which the visible line spectrum from a

hydrogen discharge tube could be obtained. A narrow beam of light from the discharge tube is passed through a prism, where the di

fferent wavelengths of light present in the

beam are separated. The line spectrum of hy

drogen consists of many different lines, but

only four are observed in the visible region. These four beams strike the photographic plate at different positions that depend upon

their wavelengths (color). The plate is

exposed at these positions, and the wavelength

of each beam can be determined very

precisely from the position of the exposure (line). If white light were used instead of the hydrogen discharge, the entire photographic plate would be exposed because all wavelengths would strike the plate.

The visible line spectrum of hydrogen gas was first observed in 1885. Similar line

spectra for hydrogen have been observed in th

e ultraviolet and the infrared, resulting in

over 40 spectral lines for the hydrogen atom. So

me atoms can have hundreds of such lines.

Johannes Rydberg discovered a single mathem

atical expression that allowed scientists

to calculate the frequency of every line in the hydrogen spectrum. The expression, now known as the Rydberg equation, is shown in Equation 2.3a:

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